The linear regression model above is based on an analysis of nutritional data from 14 varieties of cereal bars to relate the percent of calories from fat to the percent of calories from carbohydrates . Based on this model, which of the following statements must be true?
|I.||There is a positive correlation between and .|
|II.||When percent of calories are from fat, the predicted percent of calories from carbohydrates is approximately .|
|III.||The slope indicates that as increases by , decreases by .|
Select an Answer
I and II only
I and III only
II and III only
I, II, and III
The correct answer is D.
Statement I is false: Since , high values of are associated with low values of which indicates that there is a negative correlation between and .
Statement II is true: When percent of calories are from fat, and the predicted percent of calories from carbohydrates is .
Statement III is true: Since the slope of the regression line is , as increases by , increases by ; that is, decreases by .